4 29 30 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 29   c = 30

Area: T = 56.99550655759
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 7.52987196087° = 7°31'43″ = 0.13114009456 rad
Angle ∠ B = β = 71.79900431357° = 71°47'24″ = 1.25329726229 rad
Angle ∠ C = γ = 100.6811237256° = 100°40'52″ = 1.75772190851 rad

Height: ha = 28.49875327879
Height: hb = 3.93106941776
Height: hc = 3.87996710384

Median: ma = 29.43663720591
Median: mb = 15.74400762387
Median: mc = 14.26553426177

Inradius: r = 1.80993671611
Circumradius: R = 15.26444793231

Vertex coordinates: A[30; 0] B[0; 0] C[1.25; 3.87996710384]
Centroid: CG[10.41766666667; 1.26765570128]
Coordinates of the circumscribed circle: U[15; -2.82991922883]
Coordinates of the inscribed circle: I[2.5; 1.80993671611]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 172.4711280391° = 172°28'17″ = 0.13114009456 rad
∠ B' = β' = 108.2109956864° = 108°12'36″ = 1.25329726229 rad
∠ C' = γ' = 79.31987627444° = 79°19'8″ = 1.75772190851 rad

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How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 4 ; ; b = 29 ; ; c = 30 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 4+29+30 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-4)(31.5-29)(31.5-30) } ; ; T = sqrt{ 3248.44 } = 57 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 57 }{ 4 } = 28.5 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 57 }{ 29 } = 3.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 57 }{ 30 } = 3.8 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 4**2-29**2-30**2 }{ 2 * 29 * 30 } ) = 7° 31'43" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-4**2-30**2 }{ 2 * 4 * 30 } ) = 71° 47'24" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-4**2-29**2 }{ 2 * 29 * 4 } ) = 100° 40'52" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 57 }{ 31.5 } = 1.81 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 7° 31'43" } = 15.26 ; ;




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